;+ ; :Categories: ; STIX imaging and spectroscopy ; ; :Name: ; stx_livetime_fraction ; ; :Examples: ; livetime_fraction = stx_livetime_fraction( triggergram, det_select, tau_array = tau_array ) ; ; :Categories: ; STIX imaging and spectroscopy ; ; :Params: ; triggergram - a structure of 16 x N trigger accumulations where N is the number of accumulated time intervals ; may also be dimensioned to N trigger accumulations for a single detector ; IDL> help, triggergram ; ** Structure <131acfc0>, 4 tags, length=3264, data length=3264, refs=1: ; TYPE STRING 'stx_triggergram' ; TRIGGERDATA ULONG64 Array[16, 20] ;counts accumulated for each trigger for each time interval ; ADG_IDX INT Array[16] ;accumulator id's 1-16 ; T_AXIS STRUCT -> Array[1]; stx time_axis structure ; Det_select - sub-collimator numbers, 1-32 ; ; :Description: ; 28-Apr-13 gh ; ; STIX Dead Time Correction Algorithm ; ; The purpose of this writeup is to suggest an algorithm for the implementation of a STIX dead ; time correction. ; ; A careful description of the detector/ASIC performance that defines the form and approximate ; parametrization can be found in xxxxx and yyyyy. The dead time correction will be primarily ; applied on the ground, although a version may be needed for on-board correction in ; conjunction with the coarse flare locator. ; ; T = integration time during which counts were accumulated [known] ; C = number of counts in the accumulator of interest (single pixel or pixel sum) [measured] ; Cc = corrected number of counts in the accumulator of interest ; D = number of counts in the corresponding live time accumulator, which counts triggers. ; [measured] ; Tau1 = nominal readout time [known] ; Tau = (1+alpha)*tau1 = actual (or effective readout time) [assume exact value my not be ; known a priori] ; Eta1 = nominal latency time (coincidence window) [known] ; Eta = (1+beta) * eta1 = actual (or effective readout time) [assume exact value may not be ; known a priori] [depends on both energy of counts of interest and the spectrum] ; ; Nin = number of incoming photons in the period of interest [not directly measured] ; ; To be counted as a valid event in the accumulator of interest, an incoming photon must satisfy ; two conditions. ; ; First, it must initiate a trigger, the probability for which is defined as Pt. ; This is the probability that no other readout was initiated in the previous Tau seconds. ; ; D = Nin * Pt ; ; Pt = exp(-D*tau/T) ; ; Therefore ; ; Or ; ; Nin = D * exp(+D*tau/T) ; ; D = Nin * exp (-Dtau/T) ; ; Note that Nin depends on D, not C. Also, Nin increases monotonically with D. (or equivalently, ; D increases monotonically with Nin) ; ; The second condition is that if a trigger is initiated, no other photon must arrive in the ; coincidence window, the probability for which is Ps. This is the probability that no other ; photon arrived in the coincidence window. ; ; C = Cc * Pt * Ps ; ; Or Cc = C / Pt / Ps ; ; Ps = exp(-Nin*eta/T) ; ; ---------------------------------------------- ; ; Therefore the algorithm can be defined as follows: ; ; Calculate Pt = exp (-D*tau/T) ; ; Calculate Nin = D*exp (+D*tau/T) ; ; Calculate Ps = exp (-Nin*eta/T) ; ; Note that these calculations apply to any combination of pixels in a given detector pair. ; Then for the accumulator(s) of interest, calculate ; ; Cc = C / Pt /Ps ; Initially, Tau is taken as 9.6 microseconds ; Relation between STIX Event Count Rates and Live Time ; ; Assumptions: Readout time 6.6 us ; Latency time 3 us ; ; Counted Triggers Probability Input photon rate Probability Dead time Reported ; /s of trigger ph/s of single hit fraction events/s/det ; ; 100 0.9993 100 0.9997 0.0010 50 ; 1,000 0.9934 1,007 0.9970 0.0096 498 ; 5,000 0.9675 5,168 0.9846 0.0473 2,462 ; 10,000 0.9361 10,682 0.9685 0.0934 4,842 ; 25,000 0.8479 29,485 0.9153 0.2239 11,442 ; 50,000 0.7189 69,548 0.8117 0.4165 20,292 max operating point? ; 62,500 0.6620 94,412 0.7533 0.5013 23,542 ; 80,000 0.5898 135,643 0.6657 0.6074 26,628 ; 102,000 0.5101 199,971 0.5489 0.7200 27,992 max output rate ; 120,000 0.4529 264,937 0.4517 0.7954 27,100 ; 150,000 0.3716 403,685 0.2979 0.8893 22,341 ; 200,000 0.2671 748,684 0.1058 0.9717 10,582 ; 300,000 0.1381 2,172,823 0.0015 0.9998 221 ; ; :File_comments: ; Uses a default Tau, deadtime per event, of 9.6 microseconds. This may need to ; change based on tests of the Caliste detectors. ; ; :Author: ; richard.schwartz@nasa.gov ; ; :History: ; 29-april-2013, created ; 18-april-2015, richard.schwartz@nasa.gov, major revision ; 03-dec-2018, ECMD (Graz), change of calculation including eta and tau ; 03-mar-2022, ECMD (Graz), update of eta and tau values and definition tau is now only readout time ; 21-apr-2022, ECMD (Graz), added pileup correction parameter ; 17-oct-2023, ECMD (Graz), update of default eta value using empirical high trigger rate data ; 13-may-2024, P. Massa (FHNW), modified to return statistical error on live time fraction ; ;- function stx_livetime_fraction, triggergram, det_select, tau_array = tau_array, eta_array=eta_array, error=error error = 1 adg_sc = stx_adg_sc_table() default, det_select, indgen(32)+1 ntrig = (size(/dimension, triggergram.triggerdata ))[0] default, tau_array, 10.1e-6 + fltarr(ntrig) ;10.1 microseconds readout time per event default, eta_array, 1.10e-6 + fltarr(ntrig) ;1.1 microseconds latency time per event (best fit May 2023) beta = stx_pileup_corr_parameter() ; get estimate of pileup correction parameter idx_select = ( adg_sc[ where_arr( adg_sc.sc, det_select ) ] ).adg_idx ;these are the agd id needed (1-16) test_triggers = where_arr( triggergram.adg_idx, idx_select, /notequal, test_forzero ) ;which triggers to use test_triggers = ~test_forzero ;this will be true for all needed triggers for det_select ;triggergram must be sorted into adg_idx order! ix_fordet = value_locate( triggergram.adg_idx, idx_select ) ndt = n_elements(triggergram.t_axis.duration ) duration = transpose( rebin( triggergram.t_axis.duration, ndt, ntrig )) tau_rate = rebin( tau_array, ntrig, ndt ) / duration eta_rate = rebin( eta_array, ntrig, ndt ) / duration nin = triggergram.triggerdata / (1. - triggergram.triggerdata *(tau_rate+eta_rate)) nin_err = 1. / (1. - triggergram.triggerdata *(tau_rate+eta_rate))^2. * triggergram.triggerdata_err ;triggergram.triggerdata / (1. - triggergram.triggerdata *(tau_rate+eta_rate)) livetime_fraction = exp( -1.*beta*eta_rate*nin) /(1. + (tau_rate+eta_rate)* nin) ;; Compute statistical error on live time fraction livetime_fraction_err = exp(-1.*beta*eta_rate*nin) * $ abs(-1.*beta*eta_rate - 1.*beta*eta_rate * (tau_rate+eta_rate) * nin - (tau_rate+eta_rate)) / $ (1. + (tau_rate+eta_rate)* nin)^2. * nin_err livetime_fraction = livetime_fraction[ ix_fordet[sort((where_arr( adg_sc.sc, det_select,/map ))[where_arr( adg_sc.sc, det_select)])], * ] livetime_fraction_err = livetime_fraction_err[ ix_fordet[sort((where_arr( adg_sc.sc, det_select,/map ))[where_arr( adg_sc.sc, det_select)])], * ] error = 0 result = {livetime_fraction:livetime_fraction,$ livetime_fraction_err: livetime_fraction_err} return, result end